English

The geometric genus of splice-quotient singularities

Algebraic Geometry 2025-12-16 v2

Abstract

We prove a formula for the geometric genus of splice-quotient singularities (in the sense of Neumann and Wahl). This formula enables us to compute the invariant from the resolution graph; in fact, it reduces the computation to that for splice-quotient singularities with smaller resolution graphs. We also discuss the dimension of the first cohomology groups of certain invertible sheaves on a resolution of a splice-quotient singularity.

Keywords

Cite

@article{arxiv.math/0610464,
  title  = {The geometric genus of splice-quotient singularities},
  author = {Tomohiro Okuma},
  journal= {arXiv preprint arXiv:math/0610464},
  year   = {2025}
}

Comments

Two examples have been added. 17 pages. To appear in Trans. Amer. Math. Soc